Is a horse or an elephant more valuable early in the game?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws for movement, checkmate and both repetition rulings: a side that forces a repetition by perpetual check or perpetual chase loses rather than drawing. The chase half has not been validated against the official casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it before publishing.
Direct answer
The horse, and it is not close. A horse can eventually reach any point on the board and genuinely attacks; an elephant can never cross the river, at any stage of the game, and can only capture enemy pieces that come into its own half. On the standard value scale a horse rates around 4 against an elephant's roughly 2.
Why the comparison still matters
New players sometimes treat both as minor, similarly modest pieces because neither is a chariot or cannon. In fact they play completely different roles: the horse is a genuine attacking piece that just happens to be blockable, while the elephant is pure defence with no offensive ceiling whatsoever.
When the elephant's low value is misleading
A pair of mutually defending elephants can be worth protecting even at the cost of tempo, because losing both leaves horses and soldiers a clear road in. The elephant's low trade value does not mean it is safe to give away casually.
Related questions
Should I ever trade a horse for an elephant?
Rarely as an even trade, you are giving up an attacker for a defender at a real material discount to yourself.
Does the horse's value change relative to the elephant later in the game?
Yes, the horse only gets stronger as legs clear, while the elephant's value stays essentially flat throughout.